Why does the weather clock widget sometimes appear on
HTC BlinkFeed, and sometimes it doesn't?

The weather clock widget doesn't show on
HTC BlinkFeed by default.
This is because the widget panel which is your main Home screen by default already has the weather clock widget.

Once you change
HTC BlinkFeed to be your main Home screen, the weather clock widget will then show on
HTC BlinkFeed. For details, see the topic about changing the main Home screen in the user guide or how-tos.